The SmoothGrad [1]} method attempts to reduce noise in the Gradient explanation by averaging the gradient over a number of noisy copies of the original input: \(E_{SG}(m, \mathbf {x}, c) = \underset{\mathbf {z} \sim \mathcal {N}(\mathbf {0}, \sigma \mathbf {I})}{\mathbb {E}}\left[\frac{\partial m(\mathbf {x} + \mathbf {z})}{\partial \mathbf {x}}\right]\) . As the gradients of a model can change rapidly with small perturbations, SmoothGrad instead aims to find a local average of gradients. VarGrad [2]} is a variant of this method, where the variance is taken over the gradients of noisy copies instead of the expected value.
